Thesis (Ph. D.)--University of Missouri, 1929. / Vita. "Lithoprinted." Includes bibliographical references (p. 27).

Thesis (M. Phil.)--University of Hong Kong, 1998. / Includes bibliographical references.

Thesis (Ph. D.)--Cornell University.

No description available.

No description available.

A dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of requirements for the degree of Master of Science. 2015. / We consider continued fractions with coe cients that are in K, the quaternions. In particular we consider coe cients in the Hurwitz integers H in K. These continued fractions are expressed as compositions of M¨obius maps in M R4 1 that act, by Poincar´e extension, as isometries on H5. This dissertation explores groups of 2 2 matrices over K and two particular determinant type functions acting on these groups. On the one hand we find M R4 1 , the group of orientation preserving M¨obius transformations acting on R4 1 in terms of a determinant D [19],[38]. On the other hand K may be considered as a Cli ord algebra C3 based on two generators i and j, or more generally i1 and i2, where i j = k or i1i2 = k. It is shown this group of matrices over C4 defined in terms of a pseudo-determinant [1],[37] can also be used to establish M R4 1 . Through this relationship we are able to connect the determinant D to the pseudo-determinant when acting on the matrices that generate M R4 1 . We explore and build on the results of Schmidt [30] on the subdivision of a Farey simplex into 31 Farey simplices. These results are reinterpreted in H5 with boundary K1 using the group of M¨obius transformations on R4 1 [19], [38]. We investigate the unimodular group G = PS DL(2;K) with its generators and derive a fundamental domain for this group in H5. We relate this domain to the 24-cells PU and r that tessellate K. We define the concepts of Farey neighbours, Farey geodesics and Farey simplices in the Farey tessellation of H5. This tessellation of H5 by a Farey pentacross under a discrete subgroup G of M R4 1 is analogous to the Farey tessellation by Farey triangles of H2 under the modular group [31]. The result in Schmidt [30], that for each quaternion there is a chain of Farey simplices that converge to , is reinterpreted as a continued fraction, with entries from H, that converges to . We conclude with a review of Pringsheim’s theorem on convergence of continued fractions in higher dimensions [5].

Thesis (M.S. in Systems Engineering)--Naval Postgraduate School, June 2005. / Thesis Advisor(s): Roberto Cristi. Includes bibliographical references (p. 71-72). Also available online.

No description available.

Activity classification based on sensor data is a challenging task. Many studies have focused on two main methods to enable activity classification; namely sensor level classification and body-model level classification. This study aims to enable activity classification across sensor domains by considering an e-textile garment and provide the groundwork for transferring the e-textile garment to a vision-based classifier. The framework is comprised of three main components that enable the successful transfer of the body-worn system to the vision-based classifier. The inter-class confusion of the activity space is quantified to allow an ideal prediction of known class accuracy for varying levels of error within the system. Methods for quantifying sensor and garment level error are undertaken to identify challenges specific to a body-worn system. These methods are then used to inform decisions related to the classification accuracy and threshold of the classifier. Using activities from a vision-based system known to the classifier, a user study was conducted to generate an observed set of activities from the body-worn system. The results indicate that the vision-based classifier used is user-independent and can successfully handle classification across sensor domains. / Master of Science

The geometric properties of the complex numbers and the quaternions, particularly their behavior under fractional linear transformations, make them very useful for modeling certain types of geometric objects. In this thesis, we will connect the characteristics of fractional linear transformations of both the complex numbers and quaternions to the problem of developing and modifying discrete surfaces for problems in computer graphics and engineering.